My teacher gave me a "bonus" assignment the other day, and I've been racking my brain trying to solve it. Here it is:

$\displaystyle xy'(ln(\frac{x}{y}) +1) = y(ln(\frac{x}{y}) - 1)$

So far I've figured that I should substitute $\displaystyle ln(\frac{x}{y})$ for $\displaystyle u(x)$, thus giving me $\displaystyle y = \frac{x}{e^{u(x)}}$, but from there I'm kind of lost. Any ideas?